Objectives
7.1 Ratio and Proportion Express a _____ in
simplest form.
7.2 Properties of Proportions Solve for an unknown term
in a given proportion.
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Real Life Applications Let’s list on the board where you find ratios
and proportions in real life. (1st block)
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Real Life Applications Let’s list on the board where you find ratios
and proportions in real life. (3rd block)
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Definitions
Ratio The ratio of one number to
another is the _______ when the first number is ______ by the second.
Its usually expressed in simplest form.
What is looks like….. The ratio of 8 to 12 is
______, or ______. If y ≠ 0, then the ration of
x to y is _______.
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Example 2
Find the ratio of OI to ZD Using the same trapezoid…
Find the ratio of the measure of the smallest angle of the trapezoid to that of the largest angle.
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Ratios in Form a:b Sometimes the ratio of a to b is written in the form a:b. This
form can also be used to compare three of more numbers, like a:b:c.
Example: The measures of the three angles of a triangle are in the ratio 2:2:5. Find the measure of each angle.
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Slide #9
Ex. 3: Using Extended Ratios The measures of the angles
in ∆JKL are in the extended ratio 1:2:3. Find the measures of the angles.
Begin by sketching a triangle. Then use the extended ratio of 1:2:3 to label the measures of the angles as x°, 2x°, and 3x°.
J
K
L
x°
2x°
3x°
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Solution:Statement
x°+ 2x°+ 3x° = 180°
6x = 180
x = 30
Reason
Triangle Sum Theorem
Combine like terms
Divide each side by 6
So, the angle measures are 30°, 2(30°) = 60°, and 3(30°) = 90°.
Proportion
What it is… A proportion is an equation
stating that ____ ratios are equal.
When three of more ratios are equal, you can write an extended proportion.
What is looks like….
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Closure to 7.1
Ticket to stay in class
Three numbers aren’t known but the ratio of the numbers is 1:2:5. Is it possible that the numbers are:
1. 10, 20 and 50?
2. 3, 6, and 20?
3. x, 2x, 5x
Answers
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Using Proportions An equation that
equates two ratios is called a proportion. For instance, if the ratio of a/b is equal to the ratio c/d; then the following proportion can be written:
= Means Extremes
The numbers a and d are the extremes of the proportions. The numbers b and c are the means of the proportion.
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Properties of proportions1. CROSS PRODUCT PROPERTY. The
product of the extremes equals the product of the means.
If
= , then ad = bc
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Properties of proportions2. RECIPROCAL PROPERTY. If two ratios
are equal, then their reciprocals are also equal.
If = , then = ba
To solve the proportion, you find the value of the variable.
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Ex. 4: Solving Proportions
4x
57=
Write the original proportion.
Reciprocal prop.
Multiply each side by 4
Simplify.
x4
75=
4 4
x = 285
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Ex. 5: Solving Proportions
3y + 2
2y=
Write the original proportion.
Cross Product prop.
Distributive Property
Subtract 2y from each side.
3y = 2(y+2)
y = 4
3y = 2y+4
Example 7 In the figure,
a. If CE = 2, EB = 6 and AD = 3, then DB = ___
b. If AB = 10, DB = 8, and CB = 7.5, then EB =___Slide #22